ludzie is nominative and ludźmi is instrumental. Remember that you need the instrumental case after jesteście (and all other forms of być)
no. formality does not have anything to it. You are mixing languages.
It is to emphasize.
Not common, but technically correct - the sentences about "being człowiek/ludzie" without any adjective (tall, short, rich etc.) are like talking about the species in a sci-fi context.
In the beginning of the course we have little vocabulary and little grammar to choose from, so we end up with such sentences.
And anyway, it's only an accepted option here, not the main one.
"są" doesn't work with "wy".
"wy" is 2nd person plural, and 3rd person plural is either "oni" or "one".
"jesteście" is 2nd person plural (you are) and "są" is 3rd person plural (they are).